MUMBAI: HSBC Holdings Plc is shutting its private banking unit in India, marking the exit of another foreign bank from the cut-throat wealth management business in Asia’s third-largest economy. Many foreign wealth managers had scrambled to open up shop in India a few years ago and aggressively ramped up operations to take advantage of robust economic growth, only to find themselves struggling. Even though India’s economy has been minting millionaires at a strong pace, it has failed to translate into profits for the foreign wealth managers that have set up teams of well-paid bankers to help manage those riches.